The G-Exponent of a Pseudovariety of Semigroups

✍ Scribed by A Escada

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 160 KB
• Volume: 223
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1999.7993

✦ Synopsis

Ash's proof of the Pointlike Conjecture provides an algorithm for calculating the group-pointlike subsets of a finite semigroup S. We denote by P G S the subsemigroup of P S , the elements of which are the group-pointlike subsets of S. This paper is concerned with some properties of the operator G , which assigns to the pseudovariety V the pseudovariety G V generated by the semigroups P G S with S in V. As G V is a subpseudovariety of V, some of them come from properties of the power operator. We show that 3 G V = S for any pseudovariety of semigroups V that contains a semigroup such that the subsemigroup generated by its idempotents is non-permutative.